The Coleman-Hill theorem prohibits the appearance of radiative correct
ions to the topological mass (more precisely, to the parity-odd part o
f the vacuum polarization tenser at zero momentum) in a wide class of
abelian gauge theories in 2 + 1 dimensions. We re-express the theorem
in terms of the effective action rather than in terms of the vacuum po
larization tenser. The theorem so restated becomes somewhat stronger:
a known exception to the theorem, spontaneously broken scalar Chern-Si
mons electrodynamics, obeys the new non-renormalization theorem. Where
as the vacuum polarization does receive a one-loop, parity-odd correct
ion, this does not translate to a radiative contribution to the Chem-S
imons term in the effective action. We also point out a new situation,
involving scalar fields and parity-odd couplings, which was overlooke
d in the original analysis, where the conditions of the theorem are sa
tisfied and where the topological mass does, in fact, get a radiative
correction.